An alternative qualitative appreciation of science based on the holistic interpretation of mathematical symbols

Monday, August 6, 2012

Multidimensional Nature of Time and Space (5)

We have already looked at both the linear (1-dimensional) and circular (2-dimensional) perspectives on time. Once again from the 1-dimensional perspective, time is conceived in somewhat absolute fashion as having one positive direction. Then from the corresponding 2-dimensional perspective, time is conceived in relative terms as having two (complementary) directions that are positive and negative with respect to each other.

So the the nature of time conforms (in physical and psychological terms) directly with the holistic mathematical notion of dimensions, whereby each integer (representing the number of qualitative dimensions) bears an inverse complementary relationship with its corresponding number of roots with respect to unity, in quantitative terms. Thus the 2-dimensional qualitative structure (of both time and space) is inversely related to the 2 roots of 1 i.e. + 1 and - 1 (in quantitative terms).

However this mathematical notion of dimensions can then be generalised for any number giving a coherent structure for the 3, 4, 5, ... n dimensions of time (and space).

Indeed ultimately we can give meaning to the notion of such dimensions as fractional, negative, irrational (algebraic and transcendental) imaginary etc.

Thus associated with any number (in quantitative terms) is a corresponding (qualitative) dimensional meaning that intimately applies to the dynamic relative nature of both time (and space) in physical and psychological terms!

To illustrate these ideas a little further we will now look at the especially important case with respect to the true dynamic structure of time (and space) from a 4-dimensional perspective.

So 4 here (representing qualitative dimensions) is inversely complementary with the 4 roots of 1 i.e. 1 - 1, i and - i (in quantitative terms).

Now the first pair here replicate the qualitative structure associated with 2 (as representing dimensions). So once again time (and space) here have two complementary real directions that are positive and negative with respect to each other.

However the second pair i and - i are now also associated with two imaginary directions of time (and space).

Once again it may be instructive to concentrate a little on what these imaginary directions precisely entail!

In conventional scientific terms the relationship between whole and part is misrepresented in merely a conscious real fashion.

Once again as an illustration, if we take the concept of number this represents a whole notion, that potentially applies in infinite terms to all perceptions within its class. However actual numbers (as parts) are necessarily of a finite nature. So strictly, in the interaction of concept (whole) with perceptions (parts), we have the interaction of (potential) infinite with (actual) finite notions.

However in conventional scientific interpretation, the potential aspect of the whole is then reduced in a merely finite manner, with the whole concept now mistakenly assumed as applying to all actual finite part cases within its class.

So in the most general sense - as is the case with mathematical proof - Conventional Science assumes a direct correspondence in real terms as between (whole) concepts and (part) perceptions in a conscious manner. In this sense the assumed real nature of phenomena corresponds directly with the merely conscious nature of interpretation involved.

However when we understand the relationship as between concepts and perceptions in a more refined dynamic manner, we must necessarily allow for holistic (unconscious) as well as specific (conscious) aspects of experience. So strictly the experience of a concept, as potentially applying in an infinite manner, is of an intuitive (unconscious) nature, whereas the reduced interpretation of such a concept, as applying directly to all finite perceptions, is rational (conscious).

Likewise from the opposite perspective, the interpretation of an actual part phenomenon as finite and specific is rational, whereas its understanding, as in somehow reflecting the infinite whole, is once again of an intuitive (unconscious) nature.

Thus the true physical relationship of whole and part, properly entails both holistic (infinite) and specific (finite) aspects, entailing a corresponding psychological interaction that is both of an intuitive (unconscious) and rational (conscious) nature.

Now the holistic mathematical significance of "imaginary" is that it represents an indirect finite manner of representing, in physical terms, what is inherently of a potential infinite nature. In complementary psychological terms, it represents the manner of conveying what is properly of a holistic intuitive nature in an indirect rational fashion.

Thus in conventional terms, phenomena are treated in real terms as whole-parts, where every each phenomenon is interpreted in reduced quantitative terms as part of a larger whole.

However if we are to preserve the crucial qualitative distinction as between whole and part we must understand the relationship in complementary imaginary terms. Thus the part in this context - while maintaining its unique nature - reflects the infinite whole (that is qualitatively distinct). Likewise the (holistic) whole in a sense reflects all its specific parts in collective terms (again in a qualitatively distinct manner).

So in Jungian terms, each specific object is now understood in some sense as a unique immanent archetype of a universal whole (that is infinite); in reverse terms the whole, while collectively embodying all its parts, serves as a transcendent archetype, that retains a qualitative distinction.

And this two-way relationship can be indirectly expressed in rational terms as the complementarity of opposites of an imaginary nature.

Thus when we allow for the quantitative/qualitative distinction with respect to all phenomena in nature, then time necessarily possesses both real and imaginary directions that are positive and negative with respect to each other.

So from one perspective, our rational understanding of phenomena (as reduced whole/parts) takes place in real time with - relatively - positive (external) and negative (internal) directions.

However equally from a refined holistic perspective, indirectly translated in a rational manner, our intuitive understanding of phenomena (as symbols or archetypes of a more universal meaning) takes place in imaginary time with again - relatively - positive (whole) and negative (part) aspects.

Thus from the dynamic 4-dimensional (circular) perspective, time has both real and imaginary aspects with both both positive and negative directions.

And as space and time are complementary, this likewise entails that space has real and imaginary aspects with both positive and negative directions.

Now, this might seem to imply that we now have 8 dimensions in total. However in dynamic terms, the imaginary aspect of space always coincides with the real aspect of time in experience; likewise the imaginary aspect of time coincides with the real aspect of space.

Once again in experiential terms this strongly accords with Jungian notions, whereby the function that is at any time conscious in experience has a corresponding complementary shadow that remains hidden and unconscious! The clear implication of this therefore is that when the unconscious aspect of experience is not properly recognised our actual experience of phenomenal interactions in space and time becomes increasingly rigid!

So when interpreted in a more refined dynamically interactive manner, all scientific and mathematical understanding entails both real (conscious) and imaginary (unconscious) aspects in psychological terms; then in corresponding physical fashion this entails that all phenomena likewise entail both real (specific) and imaginary (holistic) aspects.

This necessarily entails therefore that all phenomena (in both physical and psychological terms) interact qualitatively in 4-dimensional time (and space) with - relatively - real and imaginary aspects (in both positive and negative directions).